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# Simple Yet Challenging

1) A caterpillar crawls up a pole 75 inches high , starting from the ground. Each day it crawls up 5 inches , and each night it slides down 4 inches . When will it first reach the top of the pole? (Taken from NSO conducted by SOF,India question Paper)

2) Victor Loh said : "The day before yesterday I was 10 , but I will turn 13 in the next year. " Is this possible? ( Taken from IQ Challenger Book)

3) Can we draw a closed path made up of 9 line segments , each of which intersects exactly one of the other segments? ( Taken from IQ Challenger Book)

4) These problems take place on an island where all the inhabitants are either "Krishna" who always tell truth or "Raavan" who always lie. ( Taken from IQ Challenger Book)

a) Person A said "I am a liar." Is he an inhabitant of our island?

b) What one question might be asked of an islander to find out where a road leads- to the city of "Krishna" or the city of "Raavan"?

c) An islander A , in the presence of another islander B , said : "At least one of us is "Raavan" ." Is a A "Krishna" or "Raavan"? What about B?

d) Several islander met at af them told the others : "You are all "Raavan"." How many "Krishna" might be there at that conference?

5) A square is inscribed in another square eeach of whose 4 vertices lies on each side of the square. The area of the smaller square is 25\49 times the area of the bigger one. Find the ratio in which each vertex of the smaller square divides the side of bigger square. (Taken from Prof. A.R.Rao Geometry Exam( only for class 10th))

6) I have three black and two white caps. I have three friends. Praful, Bihari and Trilochan. I make them stand exactly one behind another. In front is Praful, right behind him is Bihari and right behind Bihari stands Trilochan. I put a cap on the heads of each of them. Each can see the colour of the cap of people in front of him but not on his own head or on the heads of people behind him. I first ask Trilochan if he can tell the colour of his cap. He says he can’t. Then I ask the same question to Bihari. He too gives the same answer. Finally I ask that question to Praful. He is able to tell me immediately the colour of his cap. How? (Taken from a Logic book)

7) Prove that at a party, there are at least two people who are familiar with the same number of people in the party. (Taken from C.B.S.E class11th textbook)

8) I have three black and two white caps. I have three friends. Praful, Bihari and Trilochan. I make them stand exactly one behind another. In front is Praful, right behind him is Bihari and right behind Bihari stands Trilochan. I put a cap on the heads of each of them. Each can see the colour of the cap of people in front of him but not on his own head or on the heads of people behind him. I first ask Trilochan if he can tell the colour of his cap. He says he can’t. Then I ask the same question to Bihari. He too gives the same answer. Finally I ask that question to Praful. He is able to tell me immediately the colour of his cap. How? (Taken from net)

9) Three tablespoons of milk from a glass of milk are poured into a glass of tea , and the liquid is thoroughly mixed. Then three tablespoons of this mixture are poured back into the glass of milk. Which is greater now:the percentage of milk in tea or the percentage of tea in milk? (Taken from Brilliant.org)

10) Your favourite question can be added(not those types of equations solving but type of Simple problems refreshing your mind)

Note by Megh Choksi
2 years, 3 months ago

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Please edit this note and post your favorite question which are mind relaxing( simple but you enjoyed very much) · 2 years, 3 months ago

@megh choksi The first one is very easy.The answer is 71 · 2 years, 3 months ago

Yes . You too please post your favorite question thats simple and enjoyable @Anuj Shikarkhane · 2 years, 3 months ago

Nice ones. · 2 years, 3 months ago

From which CBSE book did you get the PHP question? · 2 years, 3 months ago

N.C.E.R.T class 11th textbook (Example or a question in exersice i don't know) · 2 years, 3 months ago

@megh choksi -What is this Prof A.R.Rao exam all about? · 2 years, 3 months ago

Its a geometry Exam only for class 10th students conducted by Gujarat mathematical association all over Gujarat · 2 years, 3 months ago

A request to Brilliant.org staff members

Can you make only this note public so that every user can post their question and edit it the same way as moderators do · 2 years, 3 months ago

You can ask them to post it as comments and compile it yourself and put it in the note. · 2 years, 3 months ago